New Elvet slopes up steeply as you travel south, so cycling is slow. There are two issues which make cyclists feel particularly vulnerable.
A. On the left there are diagonal parking bays by the shops, with vehicles sticking out into the road, particularly a large van which is often there. Cyclists have to give these a wide berth but then they feel vulnerable to cars wanting to overtake.
B. The second issue is the left filter on the lights to Hallgarth Street. As the road splits into two lanes, it is particularly tricky if you want to turn right into Church Street: if you stay too far left, cars overtake you and then turn across you to the left. If you manage to move over to the right the lanes are narrow and you're conscious of holding up all the cars.
A1) Remove the parking by the shops: it's not actually used much by shoppers as most vehicles have resident permits.
A2) Make the parking by the shops parallel to the road.
B1) Reduce the approach to the lights to a single lane, and abolish the left filter into Hallgarth Street. This would also make it easier for pedestrians crossing the mouth of Hallgarth Street where there is no pedestrian phase and no way to see any of the traffic lights to tell if you're safe to proceed.
Another, more radical, option would be to remodel the road layout by carving an uphill cycle lane of reasonable width through the pavement by the shops, to the left of the parking (probably realigning the parking to be parallel) and giving the cycle lane its own phase on the lights at Hallgarth Street so that cycles can get wherever they need to without conflicting with other traffic. Options for making Church Street one-way, or for private vehicle access only from the New Inn end, could also be considered.
Making Elvet Crescent two-way for bikes might reduce the need to cycle up New Elvet, but it's still the most direct route for various purposes so it's not an adequate solution on its own.