Deciding something is not a goal and if you remove the "who's reluctantly taken up a 70-year-old as an intern" bit, the plot is identical - suggesting that it's not actually necessary. BUT of course it is necessary because the film is about him.
Based on what I've looked at re: this film (I haven't seen it) is he actually the protagonist? Or is it a dual protagonist story? Either way, if the film is called "The Intern" then the intern MUST feature heavily in the logline.
Also, the inciting incident - "when faced with overwhelming..." - this isn't ONE moment. This is a build over time. So what is the one moment that changes things. Is it the arrival of this new intern? Or something that changes in the office when he arrives?
Saying "in her stead" makes it sound like she's leaving... is she?
Hope this helps.