Scripting

Assuming 9663 is the user ID, you need to join to the user table like this:

LEFT JOIN USER RESOLVER on RESOLVER.ID = HD_TICKET.CUSTOM_FIELD_VALUE3

That line would go underneath the first join to the USER table.

You can then select user attributes with RESOLVER.FULL_NAME, RESOLVER.EMAIL, etc. 

The updated query looks like this:

select HD_TICKET.ID,
       HD_TICKET.TITLE ,
        DATE_FORMAT(HD_TICKET.CREATED, '%m-%d-%y %H:%i') as TIME_OPENED,       
DATE_FORMAT(HD_TICKET.TIME_CLOSED, '%m-%d-%y %H:%i') as TIME_CLOSED,
        HD_CATEGORY.NAME as CATEGORY,
        Q.NAME AS QUEUE_NAME,
        HD_TICKET.CUSTOM_FIELD_VALUE13 as NO_DEVELOPMENT_NEEDED,
        -- HD_TICKET.CUSTOM_FIELD_VALUE3 as RESOLVED_BY,
        RESOLVER.FULL_NAME as 'Resolved By',
        HD_STATUS.NAME as STATUS, 
                   (select LDAP_UID from USER where HD_TICKET.SUBMITTER_ID = USER.ID) as SUBMITTER_NAME,
(Select LDAP_UID from USER where HD_TICKET.OWNER_ID = USER.ID) as OWNER_NAME,
ABS(DATEDIFF(HD_TICKET.TIME_CLOSED, HD_TICKET.CREATED)) + 1
     - ABS(DATEDIFF(ADDDATE(HD_TICKET.TIME_CLOSED, INTERVAL 1 - DAYOFWEEK(HD_TICKET.TIME_CLOSED)DAY),
                    ADDDATE(HD_TICKET.CREATED, INTERVAL 1 - DAYOFWEEK(HD_TICKET.CREATED) DAY))) / 7 * 2
     - (DAYOFWEEK(IF(HD_TICKET.CREATED < HD_TICKET.TIME_CLOSED, HD_TICKET.CREATED, HD_TICKET.TIME_CLOSED)) = 1)
     - (DAYOFWEEK(IF(HD_TICKET.CREATED > HD_TICKET.TIME_CLOSED, HD_TICKET.CREATED, HD_TICKET.TIME_CLOSED)) = 7) - 1 AS DAYS_OPEN_NO_WKND
from HD_TICKET
left join HD_CATEGORY on HD_CATEGORY_ID = HD_CATEGORY.ID
JOIN HD_QUEUE Q ON Q.ID = HD_TICKET.HD_QUEUE_ID
left join HD_STATUS on HD_STATUS_ID = HD_STATUS.ID
left join HD_PRIORITY on HD_PRIORITY_ID = HD_PRIORITY.ID
left join USER on HD_TICKET.SUBMITTER_ID = USER.ID
LEFT JOIN USER RESOLVER on RESOLVER.ID = HD_TICKET.CUSTOM_FIELD_VALUE3
WHERE YEAR(HD_TICKET.CREATED) in (2020) and HD_TICKET.HD_QUEUE_ID in (23,33,34,48,50,51,52,53,54,56)
order by OWNER_NAME

I see that you are using sub-select statements to get user information, which works, but I find joins to be clearer. Generally I create a join to the user table that is aliased to each type of user I want to select attributes, like this:

LEFT JOIN USER SUBMITTER on SUBMITTER.ID = HD_TICKET.SUBMITTER_ID
LEFT JOIN USER OWNER on OWNER.ID = HD_TICKET.OWNER_ID

Selecting attributes looks cleaner, at least in my opinion.

SUBMITTER.LDAP_UID as 'Submitter UID',
OWNER.LDAP_UID as 'Owner UID',

etc.