I used to play music on my iPhone using as a iPod. Several upgrades later I have lost it. I might have some still on the Apple Mac desktop. If that is the case can I easily transfer it to the iPhone?

I have the iPhone, Apple Mac and iPad all synced together through iCloud.

I did run out of memory on my iPhone which is another concern.

Most of the music was originally cd albums uploaded to the Apple Mac however my new Mac has no disc drive!

There seem to be a number of issues here, lack of storage on the phone should usually mean you can’t get any more on there, but generally when you do a backup everything should get put back.
Have you set your music up in iTunes as iTunes Match?
Why on earth have you got a computer with no disc drive? Do you mean optical drive? If so, surely any music previously ripped should be on the new Mac, or accessible via the cloud, and iTunes on the phone should show all your tracks with the little cloud icon next to them, allowing you to download them again.
How much storage has your iPhone got? If it’s something like 16Gb, I can see where there’s an issue, nobody should have smaller than 64Gb, for just this reason.
I would suggest buying an outboard optical drive, to allow you to rip new music, and burn the occasional DVD, they’re cheap as chips, and very handy; when I bought my Mac Mini six years ago I had the optical drive removed and a second HDD installed, but I bought a fast DVD writer for ripping music.
Sorry if I’m a bit confused, I’m trying to get a clear idea of what’s gone tits-up, I’m sure there will be others who have a better idea than me, I’m no wizard with computery stuff!

Still use my iPhone & iPad as an iPod, all my music is on my Mac hard drive and most of if was ripped from cd’s

Couple of thoughts;

If you have music on the mac (all macs have a hard drive/ssd btw) then you can copy it onto iPhone via iTunes
Of you bought music via iTunes store you can download direct from the internet
Of you signed up for Apple music you may find phone no longer stores music but relies on internet connection

If you’re ripped library contains som ealbums that you treasure that aren’t on Apple Music, use iTunes Match to upload them to the cloud.
Subscribe to Apple Music – no need then to worry about storage space etc. That’s how I live comfortably with a 16gb work iPhone 🙂
If t were my iPhone I’d buy the 32gb…

I did run out of memory on my iPhone which is another concern.

Na na nana na…. 😉

Subscribe to Apple Music – no need then to worry about storage space etc

Instead worry about wifi or mobile signal / battery life ?

I’m not sure what you mean – same phone losing music after several upgrades to the OS or you’ve changed phone and didn’t back up ?

Even if the latter, My wife “lost” a load of music from her phone. Was to do with itunes only showing and syncing stuff that was apple-provided. She rang them up and they talksed her through how to sort it out, music was all on hep laptop’s itunes

IANAAppleist

Thx…

New macs do not have disc drives.

I loaded Tom Tom on my iPhone and got cheapest iPhone with least memory. I pay 79p a month for extra storage.

New macs do not have disc drives.

😯

If you say so

New macs do not have disc drives.

I’m sure that what you mean is that they no longer come with an optical drive, all Macs have internal storage, either a solid-state SSD, mostly in the laptops, or normal hard-drives, or hybrid drives.
You haven’t said what flavour of Mac you have, care to give us a clue?

Well spotted Count, yes he means no optical drive !