The most common and most likely answer to this crossword clue is the 7 letter word FILLING
I've seen this crossword clue in The Times
F
I
L
L
I
N
G
Buddy explains!
The straight part
We know that "Where Americans get their gas/the dentist's chair?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case where americans get their gas/the dentist's chair? = filling.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does FILLING mean?
FILLING verb- To occupy fully, to take up all of.
- To add contents to (a container, cavity or the like) so that it is full.
- To enter (something), making it full.
- To become full.
- To become pervaded with something.
- To satisfy or obey (an order, request or requirement).
- To install someone, or be installed, in (a position or office), eliminating a vacancy.
- To treat (a tooth) by adding a dental filling to it.
- To fill or supply fully with food; to feed; to satisfy.
- To trim (a yard) so that the wind blows on the after side of the sails.
- (of a male) To have sexual intercourse with (a female).
- Anything that is used to fill something.
- The contents of a pie, etc.
- Any material used to fill a cavity in a tooth or the result of using such material.
- The woof in woven fabrics.
- Prepared wort added to ale to cleanse it.
- A religious experience attributed to the Holy Ghost "filling" a believer.
- Of food, that satisfies the appetite by filling the stomach.