Stormblessed, Dalinar gives Elhokar two sets of plate and blade captured from the parshendi. Elhokar gave them to the two warriors that were most worthy of the gear. This was likely a political move, to encourage unity in the warcamps and enhance the kingly image of Elhokar, the king being the one who provides honour and security to his subjects. The idea of giving gear to Renarin is a new one. Isn't Renarin 20? If so, he would have been 15 at the time that Dalinar gave out the gear. Add this to his "blood weakness" whatever that may be, and he would be, in the minds of most Alethi, clearly unsuited to bearing shards.
I think it's pretty clear from the text that Elhokar had his own shardblade/shardplate before the war. He was, after all, the king's son.
Think about this, Dalinar and Gavilar conquered all of Alethkar, "defeating their best shardbearers" and subduing their armies. They are likely to have captured several sets of plate and blade. Who better to receive the gear than the king's own son? Considering that he's nearly thirty by now, he would have been in his late teens/early twenties during his father's conquest, prime time to be given shards.
(Adolin's plate and blade are inherited though, right? That's what I seem to remember from his POV's)
It is likely that Elhokar already had plate/blade by the time of his father's death. He would certainly at least have had one or the other.
It seems that we have a few options for what happened to Gavilar's gear. First, the plate:
Sadaes has it,
Elhokar has it,
Or someone else took it.
Next the blade:
The Parshendi Shardbearer has it,
Shallan has it,
Someone else took it.
Of those, I think that Elhokar or Sadaes has the plate, and that the Parshendi Shardbearer has the blade. Their is, of course, one objection to the Parshendi having the blade; Dalinar would likely have recognized it. That then makes Shallan just as likely a candidate for holding the blade. Perhaps her father was in Alethkar as a traveling dignitary, and he was tipped off by the ghostbloods, followed Szeth and took the blade?