SQL regex PostgreSQL
You have LIKE and ILIKE and ~ and ~*. This covers the SQL-LIKE conditionals and the more beefy and more powerful regex-like features.

SELECT
 s,
 s LIKE '%is a sentence test%' as "like",
 s ILIKE '%is a sentence test%' AS "ilike",
 s ~ '.*is a sentence test.*' AS "~",
 s ~* '.*is a sentence test.*' AS "~*"
FROM ( VALUES
 ( 'This is a test sentence' ),
 ( 'is a sentence TeST' ),
 ( 'This a IS test sentence' ),
 ( 'iS a tEst sentence tHis' ),
 ( 'This a test sentence is' )
) AS t(s);

            s            | like | ilike | ~ | ~* 
-------------------------+------+-------+---+----
 This is a test sentence | f    | f     | f | f
 is a sentence TeST      | f    | t     | f | t
 This a IS test sentence | f    | f     | f | f
 iS a tEst sentence tHis | f    | f     | f | f
 This a test sentence is | f    | f     | f | f
(5 rows)


You're not using any advanced regex powers, so I'd go with LIKE, or ILIKE.