How have you got 2 leaves,the drawing shows 1 brick only,which is not enough. Better to build bigger pillar 330mmx215 or use steel goalpost ,and make sure foundation is acceptable.
Apologies i may not be familiar with the terminology
Here is the existing wall I'll be tieing into, on the right hand side
https://www.diynot.com/diy/media/img_20190909_112346.103263/
https://www.diynot.com/diy/media/img_20190909_112357.103265/
And the brick pier will be setup as the diagram below as stated by the SE
https://www.diynot.com/diy/media/screenshot_20190906-214006.103264/