use regular expression in if-condition in bash

if [[ $gg =~ ^....grid.* ]]

When using a glob pattern, a question mark represents a single character and an asterisk represents a sequence of zero or more characters:

if [[ $gg == ????grid* ]] ; then echo $gg; fi

When using a regular expression, a dot represents a single character and an asterisk represents zero or more of the preceding character. So ".*" represents zero or more of any character, "a*" represents zero or more "a", "[0-9]*" represents zero or more digits. Another useful one (among many) is the plus sign which represents one or more of the preceding character. So "[a-z]+" represents one or more lowercase alpha character (in the C locale - and some others).

if [[ $gg =~ ^....grid.*$ ]] ; then echo $gg; fi

Use =~

for regular expression check Regular Expressions Tutorial Table of Contents

Adding this solution with grep and basic sh builtins for those interested in a more portable solution (independent of bash version; also works with plain old sh, on non-Linux platforms etc.)

# GLOB matching
gg=svm-grid-ch    
case "$gg" in
   *grid*) echo $gg ;;
esac

# REGEXP    
if echo "$gg" | grep '^....grid*' >/dev/null ; then echo $gg ; fi    
if echo "$gg" | grep '....grid*' >/dev/null ; then echo $gg ; fi    
if echo "$gg" | grep 's...grid*' >/dev/null ; then echo $gg ; fi    

# Extended REGEXP
if echo "$gg" | egrep '(^....grid*|....grid*|s...grid*)' >/dev/null ; then
  echo $gg
fi    

Some grep incarnations also support the -q (quiet) option as an alternative to redirecting to /dev/null, but the redirect is again the most portable.