This game has 7 cards facing up in the first row and goes into descending order to the last row that has one up and 6 down. There are 3 cards left to use if no moves available. Aces go up when cleared and moves are by suit. Low cards are placed on higher ones if clear. This could mean moving many cards from one row to place on an exposed one. If a row is cleared, a king could be placed there.
It sounds like a variation of Scorpion.
Scorpion also uses 7x7 layout, but with a sub rectangle of face-down cards (the exact size varies) rather than a triangular arrangement like you describe.
And it builds King-to-Ace in place (in the tableau) rather than moving Aces up and stacking Ace-to-King above the tableau.