Taking up the suggestion by @SolarCat, if you want to shoot wildlife you could try one of the manual-focus 300mm primes, instead of a consumer zoom like the 55-300. E.g.
TAIR 3A / 300A 300mm, F4.5 Lens Reviews - Russian and Zenitar Lenses - Pentax Lens Review Database SMC Pentax 300mm F4 Reviews - K Prime Lenses - Pentax Lens Reviews & Lens Database SMC Pentax-M* 300mm F4 Reviews - M Prime Lenses - Pentax Lens Reviews & Lens Database
That would really challenge you to hone your manual focusing skills! And using manual exposure would be a learning experience too. These were top class lenses in their day and can give excellent result when used with skill (better than you could get with a 55-300 or other consumer zoom), but are much cheaper than their recent-model counterparts.
Another MF alternative would be this:
Tokina AT-X SD 100-300 f/4 Lens Reviews - Tokina Lenses - Pentax Lens Review Database
These lenses would also be a useful introduction to using relatively heavy lenses.
One more cheap tip for wildlife. Get one of these - it works brilliantly with the K-3:
https://www.pentaxforums.com/forums/22-pentax-camera-field-accessories/256288...-extender.html