Old character in love with a married postgraduate (7)
I believe the answer is:
digamma
'old character' is the definition.
(character in the early Greek alphabet)
'love with a married postgraduate' is the wordplay.
'love' becomes 'dig'.
'with' means one lot of letters go next to another.
'married' becomes 'm'.
'postgraduate' becomes 'ma' (Master of Arts is a postgraduate degree).
'dig'+'a'+'m'+'ma'='DIGAMMA'
'in' acts as a link.
(Other definitions for digamma that I've seen before include "long-retired character" , "Foreign character" .)