Half of ABBA close to having child (4)
I believe the answer is:
baby
'child' is the definition.
(synonyms)
'half of abba close' is the wordplay.
'half of' indicates taking half.
'close' becomes 'by' (I've seen this in other clues).
'abba' cut in half is 'ba'.
'ba'+'by'='BABY'
'to having' acts as a link.
This may not be right. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for baby that I've seen before include "Timid person; child" , "Very small (version)" , "Pet project" , "Comparatively small" , "This 13 [SPICE]" .)