We don't know everything about how "kingship" works in the quasi-mythical world of the Homeric epics, but most agree that "king" is a bad translation of what is going on. Laertes, Odysseus, Achilles, Menelaus, and even Agamemnon: these are not "kings" in the later historical sense, like Henry VIII. They don't rule absolutely, but instead enjoy influence according to their geras. This is a slippery term, but something along the lines of: "influence and authority derived from excellence in form (looks, wealth), and in practice (battle/contests)." They are prehistoric "strong men," more like chiefs of tribes than kings. Their "rule" is by tacit agreement of the community, and when the community decides otherwise, their influence and position are directly threatened. The geras can pass between blood relations, but not simply because of blood relation; rather, a son of a man with geras comes with pre-existing benefits, since he is associated closely with his father and possesses the amassed wealth (and hopefully the good looks) of his father.

It isn't precisely clear that Laertes ever enjoyed geras exactly, though there are off-hand references that he was of chief importance among a loose collection of islands, of which Ithaka was only one contributor. The true generator of geras in the cluster of Laertes->Odysseus->Telemachos is Odysseus, and it is he who leads the contingent to Troy. He is the hero, the one who stands out among peers both near and far. In Book 11, after his long absence from Ithaka, he openly wonders about how his geras is being treated or transferred:

εἰπὲ δέ μοι πατρός τε καὶ υἱέος, ὃν κατέλειπον,
ἢ ἔτι πὰρ κείνοισιν ἐμὸν γέρας, ἦέ τις ἤδη
ἀνδρῶν ἄλλος ἔχει, ἐμὲ δ’ οὐκέτι φασὶ νέεσθαι. (Od. 11.174-6)

“Tell me about my father and my son, whom I left behind:
does my geras still hold sway, or does some other man
have it now, because they think I won't ever return?”

Note that Penelope is not the lynchpin in this equation. Marrying her does not ensure geras, and she does not control the flow of geras from Odysseus outwards. She is a "prize" in her own right, a valuable possession, and the suitors pursue her because possession of her would elevate their own status as men of influence in the community. It isn't even particularly clear-cut that they would acquire the possessions of Odysseus, or if those possessions would pass through Penelope instead of Telemachos (but I'm not very well-versed on that aspect). For everything related to Penelope, please see the fantastic book by Felson, Regarding Penelope (1997).

Telemachos departs on his "telemachia" in part to generate his own geras, since the transmission of such from his missing father seems threatened. And he has his own ideas about what should or will happen to the "rule" of Ithaka:

"καὶ γὰρ πολλὸν ἄριστος ἀνὴρ μέμονέν τε μάλιστα
μητέρ’ ἐμὴν γαμέειν καὶ ᾿Οδυσσῆος γέρας ἕξειν." (Od. 15.521-22)

"for that man [Eurymachos]is by far the most noble left there,
and the most preferable to marry my mother and receive the geras of Odysseus."

A confusing passage, to say the least, as Telemachos says a lot here in a short stretch of words: first, he basically excludes himself from contention, but does not say why. Is it because he has no geras of his own with which to contend? Second, he chooses Eurymachos because he is aristos, best, and therefore the leading contender (along with the odious Antinoos, whom he doesn't mention). Many take this passage indisputable fact that "rule" passes through Penelope, and marrying her brings the geras of Odysseus directly. I myself don't think it is so simple, and the other evidence from the epics seem to suggest something more nuanced and complicated.

As to your question: Laertes, if he ever was "king," has been supplanted by Odysseus as the primary generator of geras in the community. In this case, the "take-over" is relatively friendly, though there is always the anxiety of father besting son in Greek mythology (cf Kronos and Ouranos, and then Zeus and Kronos).