Without fail, greaser will provide crude transport (3,6)

I believe the answer is:

oil tanker

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'without fail greaser will' is the definition.
I can't tell whether this defines the answer.

'crude transport' is the wordplay.
'crude' becomes 'oil' (I've seen this before).
'transport' becomes 'tanker' (tanker is a kind of transport).
'oil'+'tanker'='OIL-TANKER'

'provide' is the link.

Can you help me to learn more?

(Other definitions for oil tanker that I've seen before include "[See] ocean-going vessel" , "craft" , "Ship carrying "black gold"" , "Fuel transporter" , "On which crude" .)

I've seen this clue in The Times and The Sunday Times.

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