Slippery types falling over support, being less alert (8)

'less alert' is the definition.
(I've seen this in another clue)

'slippery types falling over support' is the wordplay.
'slippery types' becomes 'eels' (slippery as an eel).
'falling over' says the letters should be written backwards (letters falling back).
'support' becomes 'pier' (type of structure).
'eels' backwards is 'slee'.
'slee'+'pier'='SLEEPIER'

'being' is the link.