About dating eccentric star (3,5)
I believe the answer is:
red giant
'star' is the definition.
(I've seen this before)
'about dating eccentric' is the wordplay.
'about' becomes 're' (regarding).
'eccentric' indicates an anagram.
'dating' is an anagram of 'dgiant'.
're'+'dgiant'='RED GIANT'
(Other definitions for red giant that I've seen before include "big star" , "Large, cool bright star" , "Cool, immense star of high luminosity" , "Large low-temperature star" , "Huge Communist" .)