To answer this question we need to clarify what you mean. Do you mean: My employer allowed me to change the job?
Employer - are you employed in a company? Is this employer just one person?
Job - do you mean occupation like secretary? Or tasks/responsibilities like preparing reports?
Consider these sentences:
"Pinayagan ako ng kumpanya na magpalit ng trabaho."
- I was allowed by the company to change jobs.
Pinayagan ako ng kumpanya na magpalit ng gawain.
I was allowed by the company to change (my)tasks.
It would really be better if you could provide the context of your sentence.