Some of this depends on regiment. Mechanicus players will be much happier in any regiment that fields vehicles or specialized equipment. In addition, your choice of enemy and setting will also play into the situation. If any of this is way off base from what you are working with then my apologies in advance!
1. If your squad doesn't have a vehicle, let them find one. It doesn't have to be an abandoned Leman Russ, just a Chimera with a broken tread or even an old Land Crawler can provide a big tactical advantage. A squad taking cover behind the dozer blade is a pretty effective option. Even if the vehicle is only used for a mission, it still provides a memorable moment your tech-priest can point to.
2. Drop some Tarantulas! You can find the stats for these in Lathe Worlds and a few other non-OW supplements. These sentry guns could be dropped from orbit into a crucial area, and your squad could be sent in along with their tech-priest to awaken the machine spirits. Just when all hope seems lost against the green tide, your Tech-Priest gets the twin-linked heavy bolter turret up and running to chew apart the horde.
3. Fixed installations are just awesome. You can run some nifty haunted house style setups that see your players running around an old relay station trying to get powers, cogitators, and other systems up and running while dodging the horrors that lurk within.
4. Auspex. Throw 'em an auspex for a mission (or the improved siege auspex) This lets your tech-priest pull double duty as an ad hoc intelligence and recon source.
5. Introduce foreign weapons. Maybe the squad is working in conjunction with PDF or some oddly equipped regiment, or is on a planet where their traditional las weapons just aren't effective (constant sandstorms?) and they are issued gear that aren't really used to. Make a special pattern weapon(s) useful in this campaign or environment that are prone to issues and problems that only your handy red cloak can fix!
6. Tactical Network. Maybe the Mechanicus approaches your tech-priest about testing out new gear. Not just some new pattern or obscure tech, but a full network of targetters, pict recorders, and other systems designed to improve combat efficiency. Without any Storm Troopers nearby (or maybe they don't want to jeopardize quality troops with untested gear) the squad is asked to test them. Your Tech-Priest ends up a sort of central node to this network, flagging targets and allies, getting battlemaps up and monitoring linked in gear after the cogitators prove ineffective or broken.
7. Let the priest be the spider in the web! This one is a little more setup based, but it might be a fun side mission to throw on them. The squad is tasked with defending an important mechanicus installation that was recently reacquired from the Dominate or other enemy. It is equipped with automatic defenses, combat servitors, blast doors, and a host of other defenses... All of which must be controlled from the security room. Your Tech-Priest advises and coordinates while plugged into the system, directing servitors, handling doors, running fire suppression systems, plugging radiation leaks, and activating security systems while the squad does the face to face combat and work. Your tech-priest will probably enjoy playing with all their gizmos while still very actively being part of the squad.
8. Blowing up weird alien tech. Maybe the squad infiltrates an extremely large xenos vehicle (or their voidship is attacked and they are pressed into service as boarders) or installation. Your tech-priest is going to be the only person capable of figuring out just what any of this stuff does and which parts need to get blown up/shut down.
9. Depending on the skill layout, maybe your player could mix up combat drugs or fabricate basic parts and repairs. Just being able to get a red-dot sight without bothering the quartermaster is one of those little things that is both useful, but not hugely balance affecting.
10. The longer the squad is away from base and resupply, the more useful your tech-priest becomes. If they are behind enemy lines for potentially weeks or months, he might be their only source of charging charge packs and other basic essentials.
11. Let them counter enemy automated or mechanical security. Let them hack systems or have entirely digital conflicts against corrupted cogitators, hereteks, or other heavily mechanized enemies.
12. Borrowed from Inquisitors handbook. Technical Support - You can teamwork skill rolls (even ones you aren't trained in) so long as it involves some piece of technology. Maybe you help out the operator's drive check because you are placating the engine machine spirit.
Finally, a few thoughts on Tech-Priests and some of the difficulty that is inherent with the system. Technology is advanced and arcane enough that your TP is really the only PC that is going to have any reliable knowledge of the inner workings (Barring some Operators) so anytime high technology is really showcased it'll be their bag. On the downside, you can't have everything be about tech-use. The singular nature of the skill makes it difficult to really showcase a wide variety of options. If you as a GM are lucky, your tech-priest will have splayed those skills out some and have a wider base you can use in missions. The ability to speed repair (like first aid) isn't a huge game breaker, so long as you put some realistic limits on it. if a vehicle is destroyed or non-working, you should probably say it takes normal downtime. As for upgrading weapon damage I'd probably skip on that point and allow them a chance to tinker with quality. Let your TP make some requisition checks for superior parts and make rolls to improve common weapons up to good (or even best, but I'd make the checks very difficult) Or just let them add on attachments. You can plumb some of the DH and RT books for oddball weapons and upgrades that would fit just fine. Socially, you could even let your squad work alongside some Skitarri. That could make for a bit of fun when the tech guard just doesn't get your traditional IG troopers, but seem to adore the tech-priest (even shunting him into an impromptu sarge position)
One thing I'm pretty sold on when it comes to first timers in Only War is training. Players might not be savvy to the vast lore out there but a quick crash course on what it is like to grow up on whatever homeworld you folks pick is really easy to do. From there you have a new regiment founded (or refounded) and walk them through the entire process. They roll up characters, get assigned to a squad together, tell their families or gang or whathaveyou goodbye forever and start learning to handle that lasgun. In addition to learning lore you can also familiarize players with the rules here as they run through different training processes, get into shenanigans, maybe roast some mutants aboard the transport ship, and help build some camaraderie. Lastly, you can beat some of that suicide risk taking out of them with tactics. Only War doesn't play like Pathfinder and they'll need to make good use of cover, suppression, know how to respond to different foes, and what weapons are best for what situation. In my experience one of the things that hits new players the hardest is how quickly fear will shut down a squad who neglected WP in favor of BS and all combat talents.
TL;DR - Take them through basic training and you'll all have some educational fun.