Measure around the Pope's see, wearing his hat (10)

'measure' is the definition.
(micrometre is a kind of measure)

'the pope's see wearing his hat' is the wordplay.
I cannot quite understand how this works, but
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is located in the answer.
'see' could be 'rome' (the Holy See or See of Rome is home to the pope) and 'rome' is present in the answer.
This may be the basis of the clue (or it may be nonsense).

'around' acts as a link.

Can you help me to learn more?