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6d. 7lets .Steer mayor around contradictory parts of speech. O-y-o-a.
13d. 2 words. 6.5.Healthier drink served from tank in style. S-i-n- L---e.
23a.3lets.Worthless stuff one's left old director. T--.
24a. 11 lets. Where a few lead moulds lie.chairs go.O-i-a-c-i-s.
27a. 2 words. 1.5. Took revealing picture of adult. with yen for smut finally. I R-y-d.

last one,
X Rayed (change letter from x rated)

Thanks Trevor.

6 Down OXYMORA

Steer is OX with anagram of MAYOR (oxymora is the plural of oxymoron)

OXYMORA & TAT

13 Down is SKINNY LATTE

Anagram of tank in style

Ta(i)t

Oligarchies

Les - that's TAT(i)

Thanks everyone for your help.

It's not Bullfrog.
The director in this clue is Charles TAIT minus the i

You may be getting mixed up with the clue in the Jumbo (20across) which mentions a French Actor

Old French actor retired inside, being worried.
ag(ITAT)ed

TATI = reversed inside AGED

Old = Aged
French actor = Jaques Tati