Club offering card on initiation of members (4)
I believe the answer is:
mace
'club' is the definition.
(mace can mean a club or stick)
'card on initiation of members' is the wordplay.
'card' becomes 'ace' (ace is a type of playing card).
'on' says to put letters next to each other.
'initiation of' says to take the initial letters.
The first letter of 'members' is 'm'.
'ace' after 'm' is 'MACE'.
'offering' acts as a link.
(Other definitions for mace that I've seen before include "Spice from the nutmeg seed" , "Staff of office and a spice" , "Staff of office for a flavouring" , "Came to get ancient weapon" , "One of 9 [CLUBS]" .)