4:21 - Leia (to Kanan and Ezra): "Follow my lead and try and keep up." In Attack of the Clones, Padmé says the same thing to Anakin after they land on Geonosis: "Look, whatever happens out there, follow my lead" [1:35:51].
4:51 - Lyste (to Leia): "From what I hear, your ships have an unfortunate habit of falling into rebel hands. I assure you: that won't happen on my watch." Qui-Gon uses the same expression in The Phantom Menace; after Queen Amidala says that Senator Palpatine fears the Trade Federation wants to destroy her, he replies, "I assure you I will not allow that to happen" [1:36:33]. Palpatine uses it while talking to Mace Windu and addressing the senate in Revenge of the Sith ("And I assure you, the senate will vote to continue the war as long as Grievous is alive" [25:12] and "But I assure you, my resolve has never been stronger!" [1:35:16]) and while talking to Luke in Return of the Jedi ("I assure you we are quite safe from your friends here" [1:32:08]).
7:07 - Kanan (to Leia): "This time, you follow my lead." See above, 4:21.
7:39 - Stormtrooper (to Kanan in disguise as a stormtrooper, referring to Ryder): "We have orders to terminate one of them immediately." Referring to Leia, Tarkin gives the same command in A New Hope: "Terminate her immediately" [1:03:05]. In Return of the Jedi, C-3PO, translating for Jabba the Hutt, also uses this expression: "His high exaltedness, the great Jabba the Hutt has decreed that you are to be terminated immediately" [28:48].
13:50 - Lyste (to stormtroopers, referring to The Phantom): "This is the rebel ship we've been looking for! Set weapons for stun!" The first part of this may reference Obi-Wan's "These aren't the droids you're looking for" in A New Hope [43:39]. "Set for stun" is also said by one of the stormtroopers aboard the Tantive IV in A New Hope [6:24], and in The Empire Strikes Back, it's part of Vader's instructions to Admiral Piett: "Prepare the boarding party, and set your weapons for stun" [1:57:09].