Ajla Tomljanovic is urging Storm Hunter to concentrate on playing singles, declaring the Australian doubles ace can achieve "amazing things" if she focuses all her attention on going it alone.

After bowing out against Jelena Ostapenko on Thursday night, Tomljanovic offered a huge vote of support to world number one doubles player Hunter, now the sole remaining Aussie woman in the singles draw.

Hunter faces a tough match against Czech ninth seed Barbora Krejcikova about 9pm (AEDT) on Friday night.

"I like Storm's chances," declared Tomljanovic, while recognising it will be a battle for Hunter against the former French Open champ.

"Look, I have been telling Storm for a while now she needs to start playing singles only. She already proved she's the best in doubles — so she hasn't listened to me yet.

"I think she can do amazing things in singles."

Since Ash Barty's retirement, it's largely been Tomljanovic who has been flying the flag in the women's singles for Australia, but the former national number one has seen at close quarters in the Billie Jean King Cup exactly what Hunter is capable of.

"She's been amazing in Billie Jean King Cup over the last couple of years — and she's clutch," Tomljanovic said.

"Seeing her have success here at home is really awesome because she can play at that level, but I do think it's hard to do that when you are playing such a high level of doubles and your ranking is not quite there with your singles.

"In my opinion, she's going to have to make a decision at some point. I feel like she proved here that she really does belong at the higher level in the singles game."

As for her own future one year after being ruled out of her home Open with a knee injury that ruined most of last season, Tomljanovic felt there was a mixture of excitement and uncertainty following her 6-0, 3-6, 6-4 defeat by Ostapenko.

"It's a bit mixed. If I can kind of summarise this Aussie summer, I'm pretty happy with where I'm at and how I've responded under pressure really because as much as I'm kind of coming back, I did expect myself to play well," Tomljanovic said.

"So I definitely think I just need more court time and it will come at some point. I feel like I'm on the right track, but I have to keep working.

"When I do think back to 12 months ago, I just feel lucky that I'm here because nothing is granted once you go through something like that.

"I already kind of in my mind am excited about the next tournaments. I'm really hungry just to keep playing because my body is holding up well, and I'm super happy about that.

"I'm still in doubles [with Daria Saville], so the dream is not over yet."

As for her infamous bust-up with Ostapenko in 2021, all was sweetness and light after their latest duel.

"What happened happened in the past. It's water under the bridge now. I think there is mutual respect between her and I," Tomljanovic said.

"She was really kind with her words when we shook hands at the net and she said she was happy to see me back. As a competitor, I really appreciate. I just said good luck to her."

Dimitrov sees off Kokkinakis to leave de Minaur as only Aussie man

Earlier in the day, crowd favourite Thanasi Kokkinakis failed to reproduce his Australian Open first-round heroics, outclassed by in-form Bulgarian Grigor Dimitrov.

A packed house at John Cain Arena couldn't lift Kokkinakis to an upset win over the world number 13, who triumphed 6-3, 6-2, 4-6, 6-4.

The loss leaves Alex de Minaur as the only remaining Australian male in the tournament.

After a gruelling five-set thriller against Austrian Sebastian Ofner in the opening round, Kokkinakis said he was troubled by a hip issue that meant his serve wasn't at full power.

But he could't blame the injury for the loss.

"It was tough. He is playing incredible tennis at the moment," Kokkinakis said.

"I felt like I couldn't get the ball past him, he's moving unbelievably well.

"I just felt like I had to work for everything and got very few free points. He is definitely in some great form right now."

Dimitrov broke the South Australian early in the first two sets to set up the victory and played some flawless tennis that didn't allow the world number 80 many chances to find his way back into the match.