StringContainsQ, but anywhere in order

StringMatchQ["aabbc", "*a*c*"]

True

StringMatchQ["aabbc", "*b*a*"]

False

You can also use LongestCommonSequence to construct a function

ClearAll[strngCntnsQ]
strngCntnsQ = LongestCommonSequence[##] == #2 &;

strngCntnsQ["aabbc", "ac"]

True

strngCntnsQ["aabbc", "ba"]

False

Is this what you need?

StringContainsQ["aabbc","a" ~~ ___ ~~ "c"]

True

The following documentation pages should help you get going with string patterns in Wolfram Language:

https://reference.wolfram.com/language/tutorial/StringPatterns.html https://reference.wolfram.com/language/tutorial/WorkingWithStringPatternsOverview.html

edit Here is a function that generalizes this idea to strings of arbitrary length:

NewStringContainsQFunction[str1_String, str2_String] := 
  StringContainsQ[
    str1,
    StringExpression @@ Riffle[Characters[str2], ___]
  ]

NewStringContainsQFunction["aabbc", "ac"]
NewStringContainsQFunction["aabbc", "ba"]
NewStringContainsQFunction["aadbebfc", "abc"]

True

False

True

StringContainsQ["aaabc", RegularExpression["a.*c"]]

True