Cheaper pub involved in row (7)

I believe the answer is:

tinnier

'cheaper' is the definition.
('tinny' can be a synonym of 'cheap')

'pub involved in row' is the wordplay.
'pub' becomes 'inn' (I've seen this before).
'involved in' indicates putting letters inside.
'row' becomes 'tier' (tier is a kind of row).
'inn' inserted into 'tier' is 'TINNIER'.

I've seen this clue in The Telegraph.

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