Inject syringe's centre and roughly clean out (9)
I believe the answer is:
inoculate
'inject' is the definition.
(inoculating is a kind of injecting)
'syringe's centre and roughly clean out' is the wordplay.
'centre' indicates the central letters.
'and' means one lot of letters go next to another.
'roughly' is an anagram indicator.
The centre of 'syringe' is 'i'.
'clean'+'out'='cleanout'
'cleanout' is an anagram of 'noculate'.
'i'+'noculate'='INOCULATE'
(Other definitions for inoculate that I've seen before include "Give a jab" , "Immunise with antigens" , "Induce immunity" , "to prevent infection" , "Imbue" .)