SQL firebird dont select rows with 0
The simplest is to nest it in another select with the appropriate condition:

select ID, JobID, NAME, ORDERNUM, STARTAFTER, FINISHBEFORE, START_OFFSET_MINS, STILL_REQUIRED 
from (
    Select ID, JobID, NAME, ORDERNUM, STARTAFTER, FINISHBEFORE, 
           START_OFFSET_MINS, 
           TOTAL_MINUTES_REQ - 
                 (SELECT coalesce(SUM(TABLE_PROCESSTIMES.END_TIME-TABLE_PROCESSTIMES.START_TIME) / 60, 0) 
                  FROM TABLE_PROCESSTIMES 
                  WHERE TABLE_PROCESSTIMES.PROCESSID = TABLE_PROCESSES.ID AND TABLE_PROCESSTIMES.START_DATE &lt;= '24.04.2018'
                 ) AS STILL_REQUIRED 
    FROM TABLE_PROCESSES 
    ORDER BY JOBID, ORDERNUM
) a
where still_required &lt;&gt; 0