Is there an operator or an easy way to match an expression one or more times with the LIKE operator in SQL?

If you are talking about solving this purely in Transact-SQL, you can cover all those cases in your example data with the following filter:

WHERE FilteredField LIKE '%[a-zA-Z][0-9]'

If you want to additionally stipulate that all the characters before the numeral must be Latin letters, you will need to get a little creative:

WHERE FilteredField     LIKE           '%[a-zA-Z][0-9]'
  AND FilteredField NOT LIKE '%[^a-zA-Z]%[a-zA-Z][0-9]'

Basically, you are saying:

The value must end with a letter and a numeral, but whatever precedes the letter must not be a non-letter.

There is no way to specify this with a single condition using only built-in syntax, if that was what you were after.

As said by mustaccio in comments:

Is there anything that prevents you from using a proper regular expression implementation instead of trying to hack around LIKE?

There's an option to use CLR, Common Language Runtime, basically you create some C# functions, and you import it in your SQL server, from there on you can just call a SQL function, and it will execute your C# code for you.

This naturally gives you all the possibilies you have in .NET regex, straight from your SSMS.

There's a ton of different resources on how to go about this.
Red gate regex assembly
Code project example