Stick some publicity in this space (6)
I believe the answer is:
adhere
'stick' is the definition.
(to adhere to something is to stick to it)
'some publicity in this space' is the wordplay.
'some publicity' becomes 'ad' (short for advert).
'in this space' becomes 'here' (I've seen this in another clue).
'ad'+'here'='ADHERE'
(Other definitions for adhere that I've seen before include "Stick with header" , "Bond" , "Cling, attach" , "secure" , "'Stick to, a play say (6)'" .)