Hi kalsubu,
After testing the issue in my environment, we can refer to the following expression to achieve your requirement:
RIGHT((DT_WSTR,10)(DT_DBDATE)(TRIM([Start Date]) == "" ? NULL(DT_WSTR,10) : TRIM([Start Date])),2)+"/"+SUBSTRING((DT_WSTR,10)(DT_DBDATE)(TRIM([Start Date]) == "" ? NULL(DT_WSTR,10) : TRIM([Start Date])),FINDSTRING((DT_WSTR,10)(DT_DBDATE)(TRIM([Start
Date]) == "" ? NULL(DT_WSTR,10) : TRIM([Start Date])),"-",1)+1,2)+"/"+LEFT((DT_WSTR,10)(DT_DBDATE)(TRIM([Start Date]) == "" ? NULL(DT_WSTR,10) : TRIM([Start Date])),4)
The following screenshot is for your reference:

Thanks,
Katherine Xiong