[tomd999]

Hiya,

No, you don't need a charge pump to change the oil, a charge pump is for drawing fluid from the reservoir providing fluid to the high pressure pump inlet.

I suggest you read the following links to better understand what's going on in the hydrostatic transaxle:

Engineering Essentials: Hydrostatic Transmissions | Hydraulics content from Hydraulics & Pneumatics

Hydrostatics I – Charge! » CD Industrial Group Inc.

I also suggest you read your operators manual section on changing the fluid
OMM174377

And purchase parts service manuals for the tractor
Parts Catalog CD-ROM PC12400CD X590 Tractor Multi-Terrain Series (100001-) English

Technical Manual CD-ROM TM136919CD X590 Select Series Tractors
Worldwide Edition (100001-) English