Do I need to amend Work Permit?

Hi,

I'm here in Toronto on a closed work permit with my employer and my work permit has following clauses

1. Unless Authorized prohibited from attending any educational institution and taking any academic, professional or vocational courses.
2. Not Authorized to work in any occupation other than stated.
3. Not Authorized to work for any other employer other than stated.
4. Not Authorized to work in any location other than stated.
5. Must leave Canada by March.
6. Not Authorized to work in i) Child Care, ii) Primary or secondary school teaching, iii) Health Services. Field occupations.

and finally a remark at the bottom of the WP document

Remark : Contracted to XYZ company Canada
HSRDC #
DWO #

I continue to be employee of my employer and engagement with XYZ company is concluded. Now we have got a new customer and wanted to check if the new customer contract needs to be reflected in the WP file?

FYI - We are under the boundaries of all the 6 clauses mentioned above.

Thanks in advance!!!