Residence Permit renewal necessary? (Ankara)

With the new residence permit laws and little help from the those I called at the National Police station, I'm trying to figure out if I need to renew my residence permit.

My current employment ends May 31st. I was told my residence permit automatically expires on that date (RP expiry date it 3/17/ Protected content that I need to renew it. I received contradictory information from my current employer.

I will start a new job in Istanbul in August of this year. Anyone know if I need to renew my residency permit to stay in Turkey until the start of my new job?