The TR4A was introduced in 1965. It was an update of the TR4, which had been around since 1961. The biggest change was the chassis, which had a new independent rear suspension.
When Triumph introduced the TR4A, the dealers were afraid that their customers would not like the new independent rear suspension. They convinced Triumph to offer the TR4A with an optional live rear axle, very similar to the one found on the old TR4. Triumph obliged. By most accounts 25% of the TR4As were ordered with the live axle.
The only glaring flaw I can find in this car is the satellite radio unit sticking out of the dash. What's up with that? This is a 1967 Triumph... The only sounds you should be listening to are the sounds of the engine and the sound of air coming over the top of the windshield and past your ears.
I guess if you decide to take this car on a cross country trip (how cool would that be?) and want to find out what the weather is like 200 miles ahead, a satellite radio could be useful. Or, you could just rip the thing out and take your chances, just like everyone did back when this car was new. That's what I'd do.