Moving to another rank, bishop checking again (10)

'moving' is the definition.
The answer and definition can be both to do with social activities as well as being present participle verbs.
Maybe they are linked in a way I don't understand?

'another rank bishop checking again' is the wordplay.
I cannot quite understand how this works, but
'another' could be 're' (I've seen this in other clues) and 're' is located in the answer.
'bishop' could be 'b' (chess abbreviation) and 'b' is present in the answer.
The remaining letters 'vetting' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

'to' is the link.

Can you help me to learn more?