Beat province's top university, one in capital (5)
I believe the answer is:
pulse
'beat' is the definition.
(synonyms)
'province's top university one in capital' is the wordplay.
'top' indicates taking the first letters.
'university' becomes 'u' (abbreviation for university).
'one in capital' becomes 'lse' (I can't justify this - if you can you should give a lot more credence to this answer).
The first letter of 'provinces' is 'p'.
'p'+'u'+'lse'='PULSE'
(Other definitions for pulse that I've seen before include "A general opinion" , "edible seeds of leguminous plants!" , "Heart beat - peas, beans etc" , "Musical beat; edible seeds" , "Series of rhythmic beats" .)