Even if there isn't an upfront allowance, being your own gear. Make your boss some money and become productive. Then go back to table and ask for some help with acquiring some upgraded or improved gear. He had no clue if you will stick with the opportunity or make off with a pile of new stuff he bought you. Learn, advance, keep note of your progression, then sit down and ask him to invest more into you. He's actually making an investment already and truth be told, his return on investment is likely slim at the moment.
When I started climbing, I ran out and bought gear. I fumbled through some super easy stuff for my boss. I believed that suddenly I was worth a lot more. It took a few years to look back and realize that while I had loads of ambition, and a lot of knowledge from a lifetimes exposed to tree work, I wasn't jack shit for a cash cow when it came to beig in the tree itself. But he invested in me even without a pay increase. A lot of jobs bid for 2 hours, took 3-5 hours with me at the wheel. He was spending more money. It just wasn't going right into my hand. It was going into my future and the immediate future of his company as well. Both parties will have skin in the game. The intention is that both parties have a future gain though.