Become less dense and almost go to university at Cambridge finally (9)
I believe the answer is:
attenuate
'become less dense' is the definition.
(attenuate can mean to become thinner)
'almost go to university at cambridge finally' is the wordplay.
'almost' means to remove the last letter (most of the word but not all of it).
'go to' becomes 'attend' (synonyms).
'university' becomes 'u' (abbreviation for university).
'at' means one lot of letters go next to another.
'cambridge finally' becomes 'ate' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'attend' with its final letter taken off is 'atten'.
'atten'+'u'+'ate'='ATTENUATE'
'and' is the link.
(Other definitions for attenuate that I've seen before include "become weak" , "Slender" , "Reduced" , "Reduce (a signal)" , "Dilute" .)