Half of inked design around middle of her nipple (4)
I believe the answer is:
teat
'nipple' is the definition.
(synonyms)
'half of inked design around middle of her' is the wordplay.
'half of' indicates taking half.
'inked design' becomes 'tattoo' (I've seen this before).
'around' is an insertion indicator.
'middle of' says to take the centre.
The centre of 'her' is 'e'.
'tattoo' cut in half is 'tat'.
'tat' going around 'e' is 'TEAT'.
(Other definitions for teat that I've seen before include "Bulb on infant's bottle" , "Part of feeding bottle" , "Piece on baby's bottle" , "essential for babies" , "Nipple or dug" .)