Didn't Steve Cram train there so I'm assuming it's a 400 metre track sort of size. Loads of investment in South Shields in recent years. I've been involved in some of the grant funded stuff and about to invest another £80m. South Shields is one of the most socially deprived area's in the country so the funding opportunities are there as it's easier to prove improved economic benefit in a deprived area. i.e. will it bring jobs directly at the stadium or indirectly in shops and hotels.
The council do want to attract more visitors, they put on free events in Bents Park for example. They want it to be a proper seaside resort Would a speedway team attract the type of numbers who'd spend enough money to improve the local economy? Enough to offset against 'noise'? And floodlights might be an issue. I can't see permission being given for 7 days a week operation so it couldn't be used for training. If I recall there are some new housing developments and some expensive housing very close by (to the West not many to the East). It's effectively the posh end of South Shields. It really would be a cracking day out. Amusement Park, Beach, Fish & Chips or Ocean Road curry (both if you're THJ). Despite being almost in the sea it's quite accessibly by road (tunnel) or train or even Ferry!! Although it's a bit of a walk from the river.
The council are supportive of the Mariners progressing up the football pyramid as it will attract more visitors from outside of the region. On that basis having a sports team in a national competition is ideal. An authority like South Tyneside is never going to attract top level sporting events (apart from GNR which it's lost in 2020 and 2021) so having a team in a national competition would appeal, especially one which has moved from a neighbouring authority.
Grants for Sporting facilities are outside of my remit but I think they tend to be linked to community based projects and are probably therefore smaller than the cost of building a speedway track and refurbishing a stadium. You'd need a significant local contribution regardless.
Certainly worth investigating the possibility because it could be a really good solution. But you need to be able to demonstrate how the area would benefit economically and what it would offer the community (reducing crime, improving skills etc).
PS it's right where the Great North Run normally ends for those not familiar with the area.