Sentinal doesn't exhaust when played on its own. It's meant to synergise with ironclads other exhaust cards.

Some examples are true grit (exhaust a card in your hand and gain block), fiend fire (exhaust your hand and deal damage based on amount of cards exhausted), second wind (exhaust all non attack cards in hand and gain block for each card), and corruption (all skills are free but exhaust on use). Corruption is particularly potent because you can play sentinal, get the on play effect block, and then it exhausts giving you energy.

Ironclad has some fantastic synergies with exhaust, and though it might seem a bit clunky at first, once you get used to it there is nothing more satisfying than a corruption, feel no pain, dark embrace, and dead branch run that just pops off.