Change your command lke below.
$ [[ $a =~ [A-Za-z]+ ]] && echo "YES ITS STRING"
YES ITS STRING
Use =~ operator to test an input string against a regex.
Add + next to the character class, so that it would repeat the previous pattern or token one or more times. Here it's unnecessary.
Add anchors , in-order to do an exact string match. [[ $a =~ [A-Za-z] ]] && echo "YES ITS STRING" alone will print the string YES ITS STRING because the variable a contains atleast an alphabet.
$ a="HelloWorld"
$ [[ $a =~ ^[A-Za-z]+$ ]] && echo "YES ITS STRING"
YES ITS STRING
$ a="Hello World"
$ [[ $a =~ ^[A-Za-z]+$ ]] && echo "YES ITS STRING"
$