If the skipping started happening right after you replaced the chain, I would suspect that the cassette needs to be replaced. If the chain has excessive wear, it causes a wear pattern on the cassette that will prevent the chain from engaging properly under heavy pedaling load. It is hard to discern this wear pattern by visual inspection.

This situation can be avoided by replacing the chain before it's worn excessively. When the chain wears, the wear is on the pins, so the chain gets longer. The chain should be replaced before the increase in length is 1%.

Wear can be checked by measuring the length over a number of links using an accurate scale. The pitch (distance between the centers of pins) is 1/2 inch, so a new chain should measure 12 inches over 24 links. The chain should be replaced before this measurement reaches 12 + 1/8 inches.

Alternatively, there are special chain wear measurement tools made for this purpose.

If the skipping started happening right after you replaced the chain, I would suspect that the cassette needs to be replaced. If the chain has excessive wear, it causes a wear pattern on the cassette that will prevent the new chain from engaging properly under heavy pedaling load. It is hard to discern this wear pattern by visual inspection.

This situation can be avoided by replacing the chain before it's worn excessively. When the chain wears, the wear is on the pins, so the chain gets longer. The chain should be replaced before the increase in length is 1%.

Wear can be checked by measuring the length over a number of links using an accurate scale. The pitch (distance between the centers of pins) is 1/2 inch, so a new chain should measure 12 inches over 24 links. The chain should be replaced before this measurement reaches 12 + 1/8 inches.

Alternatively, there are special chain wear measurement tools made for this purpose.