Rubbish head of state and others from the Right (5)
'rubbish' is the definition.
(I've seen this before)
'head of state and others from the right' is the wordplay.
'head of' suggests taking the first letters.
'and others' becomes 'etal' (synonyms).
'from the right' shows that the letters should be reversed in order.
The initial letter of 'state' is 's'.
'etal' reversed gives 'late'.
(Other definitions for slate that I've seen before include "A roof-tile; criticise heavily", "Metamorphic rock that can be split into thin layers", "Stone used for roofing", "list of candidates", "Roof tile or pub credit".)