As noted, there is
a spell for opening doors, gates and locks already.
I won't answer "Yes" or "No" for Telekinesis specifically, but RPing of most spells and spell effects that are not mechanically represented
may be possible under the supervision and direction of a GM. This means it is up to the GM to decide whether or not something of the sort can be attempted and up to that GM the attempt is successful. The answer may vary from GM to GM, but the possibilities exist.
It should be remembered that RPed spells and spell effects are not "free". Magic has a cost, of course, and such an RPed spell should reduce the available spells a caster has for a given level.
For example, Telekinesis is a 5th level Transmutation spell for Wizards and Sorcerers. If I were asked, a caster who could not cast 5th level spells...or one who already cast all of his 5th level spells...or who was a Conjuration specialist Wizard...or a Bard...would not be able to attempt such a thing, in my opinion. The higher the level of spell requested, the more difficult I would make it. For a wizard, I might require the wizard to prepare the spell, thus sacrificing another.
I personally wouldn't let Clerics attempt Telekinesis, just like I wouldn't let Wizards attempt Cure Critical Wounds.
Druids of sufficient level could potentially combine Plant Growth (3rd level) with Animate Plants (7th level) to do what you suggest.
Other GMs may have different methods and different answers.
So things like this are possible (and have been done), but one must work with a GM, and within the constraints set by that GM, to make them happen.