What does get posh digs mean?

The phase uses 2 differing slang terms normally found in the UK.

"Get" means of course to obtain

"Posh" is an acronym for PORT OUT, STARBOARD HOME. This was a term used for rich shipping passengers who would use the port cabins leaving their destination and the starboard when coming home. This was because the sun was in the port side out and starboard side coming home. The term "posh" was then used for anyone who had a wealthy lifestyle.

"Digs" this is a slang term for a boarding room, hotel room or a bed and breakfast establishment.

The phrase therefore means "to obtain upperclass accommodation"