Unless you have some way of making it an animal companion or cohort you're pretty limited in what you can do with it. By the RAW it will not advance as you do. This means that it will not gain any additional skills, feats, or even hp. You could load it up with a bunch of magic items, spells, buffs, etc. But, in any campaign it won't be long before enemies are throwing around attacks that's minim damage will be greater than your pet's total hp. Meaning if enemies are given any reason to attack it, it will easily die in 1 round without you being able to do much about it.
Unless you want to multi-class into something that gets an animal companion your options are fairly limited.
You might be able to get DM approval to gain it as an animal companion via
Nature Soul + Animal Ally
or
Exotic Heritage[k. nature] + Eldritch Heritage[Sylvan]
Both require approval, though for different reasons. Animal ally doesn't have Deinonychus as an option and Slyvan goes against the RAI in terms of being a choice for Eldritch Heritage.
If you don't care about it gaining feats and you just want to give it survivability and for it to have some combat utility you could instead take it as a familiar (just use the stats for Compsognathus and re-flavor it as a Deinonychus). To this end you could gain a familiar via
Skill Focus[k. any] + Eldritch Heritage[Arcane]
or
Iron Will(feat) or House of Green Mothers Pupil(Trait) + Familiar Bond + Improved Familiar Bond
In either case you would then have the familiar take the mauler archetype which would allow it to grow to be a medium sized creature.
On a side note, I have never played Hell's Rebels so all of my advice is for a generic campaign. I don't know if there is anything specific to that AP that would be available as another option.
The only other option I can think of is to ask your DM if it can act as your cohort via the Leadership feat (or since you're only 2nd level the Page feat)
edit: I just realized that the Page feat can't be taken until 4th level so that may not actually be an option worth considering.
You could get awaken animal cast on it. From there it should be able to gain class levels, but it would have no special reason to obey you. It could easily just decide to go back to the wild.
Taxidermy?
Better yet, necromancy.
Well, the awakened creature does things for the caster. But I'm assuming you'll need to hire a druid to cast it for you. And that druid may eventually want to awaken some other creature.
This is a fantastic choice given the ap