Squeeze, see, in a big way (6)
I believe the answer is:
hugely
'in a big way' is the definition.
(huge means big)
'squeeze see' is the wordplay.
'squeeze' becomes 'hug' (synonyms).
'see' becomes 'ely' (see is a place with a cathedral - e.g. Ely).
'hug'+'ely'='HUGELY'
(Other definitions for hugely that I've seen before include "Immensely" , "To a very great extent" , "in a big way" .)