It is very clear, that this Hadith is not restricted to that period of absence while Rasulullah (SAWA) was at Tabuk. Secondly, Rasulullah (SAWA) is indirectly saying that Imam Ali (a.s) will continue to hold that position of Harun toward Moosa, even after his passing, with one exception being that there will be no further Prophet.
According to Afosa.org, what Rasulullah (SAWA) is saying is that if Harun would have outlived Moosa, then he would have been Nabi and Imam at the same time. However, Imam Ali (a.s) will not be a Nabi, but he will be an Imam. This is the crux of what this Hadith is saying.
What is really important and interesting is that Hadith resources have recorded that this statement of Rasulullah (SAWA) in reference to the status of Imam Ali (a.s) was repeated on multiple occasions. I will list a few below.
a. It is reported from the second Caliph, Umar ibn Khattab, that he saw someone swearing on Ali (a.s). Umar says that he thought that this person is a hypocrite, because he says that he heard directly from Rasulullah (SAWA) the above-mentioned statement, that the status of Imam Ali (a.s) is like that of Harun to Moosa, except that there will be no further Prophet.
Now, if this is not a virtue and status of Imam Ali (a.s) being prescribed, then why does the second Caliph, Umar ibn Khattab, refer to the person who is abusing Ali (a.s) as a hypocrite, based upon this Hadith?
b. On the day in Mecca when Rasulullah (SAWA) made companions as brothers to each other, and made Imam Ali (a.s) as his brother, he again repeated this statement, of Imam Ali (a.s) being to him like Harun to Moosa (a.s), except that there will be no Prophet after him.
c. Then, when Rasulullah (SAWA) established brotherhood between the Muhajir and Ansar, he again selected Ali (a.s) to be his brother, repeating the same statement.
d. Ummi Saleem was a truly great personality from the history of Islam with enormous sacrifices with immediate loved ones like her father and brother martyred. Her husband never accepted Islam, and she therefore left him. Rasulullah (SAWA) would sometimes visit her to check-in, given the stress she was going through.
During one of these visits, history has recorded that Rasulullah (SAWA) again echoed this statement about the status of Imam Ali (a.s), saying that the flesh of Ali (a.s) is from his flesh, and the blood of Ali (a.s) is from his blood, and Ali (a.s) is to him like Harun is to Moosa (a.s).
e. Ibn Abbas narrates from the second Caliph, Umar ibn Khattab, who said that one should not speak bad about Imam Ali (a.s), because he heard 3 statements about Ali (a.s) directly from Rasulullah (SAWA). Umar ibn Khattab goes further to say that if he had one of these three, then it would have been better for him than anything else in this world.
Umar ibn Khattab explains that he was there with the first Caliph and a group of other companions (Sahaba) in the company of Rasulullah (SAWA). At this occurrence, Umar ibn Khattab narrates that Rasulullah (SAWA) placed his hand on the chest of Ali (a.s) saying to Ali (a.s) that he is the first believer and to him like Harun is to Moosa (a.s).
f. Nisaa’i was a great Sunni scholar and he explains an incident where Ali (a.s), Jafar and Zaid were discussing the guardianship of the son of Sayyidina Hamza (r.a). Naturally, many people lined up for this, given the status of Sayyidina Hamza (r.a) and his martyrdom for Islam in the Battle of Uhud. At this point, Rasulullah (SAWA) repeated the statement to Imam Ali (a.s), that he is like Harun to Moosa (a.s), except that there will be no Prophet after him.
g. Again, on that day, when all the doors of the different houses which opened to the mosque of the Prophet in Madina, namely Masjidun Nabawi, were closed, and the only door which was kept open was that of Imam Ali (a.s), Rasulullah (SAWA) said to Imam Ali (a.s) that what is Halaal for him is Halaal for Ali (a.s), and that Ali (a.) is to him like Harun to Moosa (a.s), except that there will be no Prophet after him.
We can see here, that this statement about the virtue and status of Imam Ali (a.s) is not confined to the Battle of Tabuk, since it was repeatedly noted by Rasulullah (SAWA) at various points in history, as noted above.