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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE POWERMART SYSTEM "powrmart.dtd">
<POWERMART CREATION_DATE="12/01/2016 17:43:15" REPOSITORY_VERSION="184.93">
<REPOSITORY NAME="PCREPO_BIDEV" VERSION="184" CODEPAGE="UTF-8" 
DATABASETYPE="Oracle">
<FOLDER NAME="ABC" GROUP="" OWNER="Administrator" SHARED="SHARED" 
DESCRIPTION="" PERMISSIONS="rwx---r--" UUID="3b13d2c9-39dc-426f-8320- 
def2bb8424ef">

I have the above sample data. In which file will have FOLDER NAME with some value. I have to replace it with some other value which is a variable
I want to replace FOLDER NAME="ABC" with DEF

 sed -i "s/<FOLDER NAME="*"/<FOLDER NAME="$FLDR"/g" Gather.XML

Above sed commands doesn't through any error but it is not replacing.

Try this,

sed -i 's/<FOLDER NAME="[A-Z]*"/<FOLDER NAME="'$FLDR'"/g' Gather.XM

Assuming this is a well-formed XML document, using XMLStarlet:

xmlstarlet ed -u '/POWERMART/REPOSITORY/FOLDER[@NAME="ABC"]/@NAME' -v "$FLDR" file.xml

This would locate the FOLDER node under /POWERMART/REPOSITORY whose NAME attribute is ABC and change its value to the value of the shell variable FLDR.

Example:

$ cat file.xml
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE POWERMART SYSTEM "powrmart.dtd">
<POWERMART CREATION_DATE="12/01/2016 17:43:15" REPOSITORY_VERSION="184.93">
 <REPOSITORY NAME="PCREPO_BIDEV" VERSION="184" CODEPAGE="UTF-8" DATABASETYPE="Oracle">
 <FOLDER NAME="ABC" GROUP="" OWNER="Administrator" SHARED="SHARED" DESCRIPTION="" PERMISSIONS="rwx---r--" UUID="3b13d2c9-39dc-426f-8320-def2bb8424ef"/>
 </REPOSITORY>
</POWERMART>

$ FLDR='DEF'
$ xmlstarlet ed -u '/POWERMART/REPOSITORY/FOLDER[@NAME="ABC"]/@NAME' -v "$FLDR" file.xml
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE POWERMART SYSTEM "powrmart.dtd">
<POWERMART CREATION_DATE="12/01/2016 17:43:15" REPOSITORY_VERSION="184.93">
 <REPOSITORY NAME="PCREPO_BIDEV" VERSION="184" CODEPAGE="UTF-8" DATABASETYPE="Oracle">
 <FOLDER NAME="DEF" GROUP="" OWNER="Administrator" SHARED="SHARED" DESCRIPTION="" PERMISSIONS="rwx---r--" UUID="3b13d2c9-39dc-426f-8320-def2bb8424ef"/>
 </REPOSITORY>
</POWERMART>

If you have to match a particular REPOSITORY's NAME, then e.g.

xmlstarlet ed -u '/POWERMART/REPOSITORY[@NAME="PCREPO_BIDEV"]/FOLDER[@NAME="ABC"]/@NAME' -v "$FLDR" file.xml

You are missing a "." in your sed expression to match all characters

 sed -i "s/<FOLDER NAME=".*"/<FOLDER NAME="$FLDR"/g" Gather.XML

It looks like you should do [^"]* instead of *:

sed -i "s/<FOLDER NAME="["]*"/<FOLDER NAME="$FLDR"/g" Gather.XML

Since you want to match all text till the first " there. * will match the literal * character, but you don't have that there, so the file's contents never match.