The right side of a "Variable Assignment" is considered quoted (no splitting or globing):
LESS=+'/A variable may be assigned' man bash
A variable may be assigned to by a statement of the form:
name=[value]
Word splitting is not performed, ... . Pathname expansion is not performed.
Therefore:
$ var=*
$ echo "$var"
*
To get an asterisk to expand, you need to use it un-quoted:
var="$(echo *)" ### Expand to the list of files on pwd.
In your case:
$ ID=one
$ IMP="$( echo "[email protected]:/data/$ID/EER_DATA/"*"/ImpostorScores.txt")"
$ echo "$IMP"
[email protected]:/data/one/EER_DATA/something/ImpostorScores.txt
That something will be expanded if the whole path match, that is, a tree like this actually exists:
$ tree [email protected]\:/
[email protected]:/
└── data
└── one
└── EER_DATA
└── something
└── ImpostorScores.txt
Note: I removed the second $ID from your source, easy to re-place.