Gloucester road tube station... are there escalators?

No, there are stairs. I’m estimating about 2 dozen or so from the District line platform to the ticket hall. The ticket hall is at street level.

I found this photo which shows the staircase in the Gloucester Road tube station.

https://www.gettyimages.com/detail/news-photo/gloucester-road-underground-station-london-england-news-photo/982765876

The circle line (and of course the lines it shares tracks with) were built as "cut-and-cover", just below street level, and in some places in cuttings. You can see in the photo there is daylight shining in. These stations generally have steps up to the surface.
The deeper tube lines have escalators, but in some cases there are stairs from the street down to the "booking hall" just below ground level where the ticket barriers are, and separate escalators from there down to the individual lines.

That is a generalisation, but mostly true.

That is true from an historical perspective, but a number of Circle/District/Met stations do have either escalators or lifts from street level to the platforms that have been added over the years, the nearest to Gloucester Road being Earls Court, which was completed for the 2012 Olympics. Some only have them for some direction of travel (eg West Brompton) and some have escalators only going up (eg Sloane Square).

Gloucester Road has a lift down to the deep-level Piccadilly Line platforms.

tfl.gov.uk is a gold mine of information. https://tfl.gov.uk/transport-accessibility/ is a good hub for anything that makes your journey easier.

Even with the lift, there are still some steps from the lift to the Piccadilly line platform.

You all are truly amazing to take the time to help me. Laura, that picture is wonderful! Thank you so very much!!!