I would like to apply for GP recruitment in upcoming round 1

I would like to apply for GP recruitment in upcoming round 1.

I am little bit confused about my visa status for the period between I am finishing here and joining GP training ( if selected)

My present visa ( on Tier 2 visa ) will expire on 21stJune 2019.

Now if I get selected in round 1, I believe the COS from deanery will have a start date from 1st August 2019.

So there is a period of 1 month that I would like to stay here in UK legally ( without going back to home country) and avail that GP training post from August 1st ( if get selected).

Could you please suggest me options to cover that period ?

Would the hospital be happy to extend my contract with them for such a short duration ?

Any 1 with similar situation and experience ?