EU work permit from UK

[Eurus]

Hello,
I am on TIER4 student visa in UK and my graduation will be in January and my visa also expires right after that. I have got a job in EU country and have started the visa process from here in UK but as the visa processing time mentioned on the website is 2-3 months. I wanted to know in case my visa comes after my residency expires for UK, is there anyway for me to receive my work permit here from UK?

Thanks

[CR001]

You must leave the UK on or before the expiry date of you student visa. If you don't, you will be an overstayer.

If you don't have a valid visa of some sort, you obviously cannot come back to the UK to get your work permit visa.