Girl the eccentric RA has (5)
I believe the answer is:
sarah
'girl' is the definition.
'the eccentric ra has' is the wordplay.
'the eccentric' is an anagram indicator.
'ra'+'has'='rahas'
'rahas' anagrammed gives 'SARAH'.
(Other definitions for sarah that I've seen before include "Girl's name" , "Abraham's wife in the Old Testament" , "Abraham's wife (OT)" , "Lady" , "Woman" .)