Kingdom offering enjoyment starts to get irresponsible (5)
I believe the answer is:
fungi
'kingdom' is the definition.
(I know that Fungi is a type of kingdom)
'enjoyment starts to get irresponsible' is the wordplay.
'enjoyment' becomes 'fun' (enjoyable activities).
'starts to' suggests taking the first letters.
The initial letters of 'get irresponsible' is 'gi'.
'fun'+'gi'='FUNGI'
'offering' acts as a link.
(Other definitions for fungi that I've seen before include "Yeasts, moulds, mushrooms etc" , "life in woodland?" , "Maybe moulds" , "Spore-producing organisms" , "Eg, toadstools" .)