The lab parameters you describe (slightly elevated TSH, normal T3/T4) in isolation are an indication of latent hypothyroidism.
In general, this is interpreted as a thyroid gland not functioning optimally anymore; and thus more TSH is needed to stimulate the production of physiological T3/T4 levels. The current viewpoint is that this compensation mechanism is only temporary and at some point, the thyroid will likely fail to produce enough T3/T4 even with more TSH stimulation and hypothyroidism ensues.
(Side note: This is why usually always T3/T4 (levothyroxine) are supplemented and not TSH, as the high TSH is an indication that the thyroid gland is not sufficient in producing T3/T4).
In itself, a moderately raised TSH value (>4 <10 mU/L) on its own is not a health condition requiring treatment, but the risk does exist that the patient will go on to develop overt hypothyroidism with its potential for associated cardiovascular sequelae (8, 9, e1, e2). The treating physician must therefore decide whether to leave the patient untreated, or to treat the patient even though there is no clear indication for doing so and the risk is of triggering iatrogenic hyperthyroidism.
The linked review (albeit a bit dated) nicely discusses some points for shared-decision making whether to start T3/T4 supplementation or not.
Elevated TSH levels above >10mU/l but still normal T3/T4 levels are less common, the article goes to mention here that
[i]n some studies, subclinical hypothyroidism has been shown to be an independent risk factor for the development and exacerbation of heart failure and coronary heart disease (9, e1, e2). However, a clear relationship was demonstrated only in the patient group =70 years of age with subclinical hypothyroidism and a TSH value >10 mU/L (29, 30, e1, e34– e36), so it is only for this patient group that a treatment recommendation can be made.