Just a bit of a headcanon for Heart ( Ianto’s Doctor Why AU )
Their motto was “the story changes, the ending stays the same”: their operatives protected the Web of Time by ensuring, by whatever means, that the net result of history remained constant, even though details might change.
He left because of the agency, because of their missions. The Celestial Intervention Agency never settled well with him. He did everything by the book, but sometimes they have to go far to properly ensure that the timeline stays the same. It sometimes meant removing someone or undoing something. Heart completely obeys the Laws of Time by heart. “Ensuring that the Web of Time is protected at all costs.” He’d told himself in order to stop the guilt from spilling. I’d like to think some of the rare missions they undergo did however involve just a tiny smudge of murder. Not every thing on Gallifrey is a saint, let’s be honest. Sometimes it involves a little treason, a bit of this, a bit of that.
And eventually he had enough.
So off he went, leaving everything behind ( not without stealing certain stuff like certain plants and their seeds ) and then making his way to earth. There he started his new life. A businessman at first, eventually Lisa was the inspiration for his coffee shop: The Welsh Grounds in Cardiff.