Nurse having bad luck filling empty syringe (6)
I believe the answer is:
suckle
'nurse' is the definition.
('suckle' can be a synonym of 'nurse')
'bad luck filling empty syringe' is the wordplay.
'bad' is an anagram indicator.
'filling' means one lot of letters goes inside another.
'empty' suggests removing the centre.
'syringe' with its centre removed is 'se'.
'luck' anagrammed gives 'uckl'.
'uckl' inserted within 'se' is 'SUCKLE'.
'having' is the link.
(Other definitions for suckle that I've seen before include "Nurture" , "Feed from a teat" , "Breastfeed" , "Feed (baby) from breast" , "Nurse" .)