I have enabled the compose key using the standard GNOME [Compose][a][e]
gives æ; [compose][-][a]
gives ā
; [compose][-][a][e]
gives āe
, and [compose][a][e][-]
gives æ-
; is it possible, however, to obtain æ with a macron as it is to obtain e.g. ā
, ē
, &c.?

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2 Answers
Yes. One built-in way to do it is:
Compose followed by _ followed by æ => ǣ
But if you don't have æ easily accessible in the keyboard layout you are using, you can create an ~/.XCompose
file as Characters writing mentioned and add for instance this line:
<Multi_key> <underscore> <a> <e> : "ǣ" U01E3 # LATIN SMALL LETTER AE WITH MACRON
At next login you should be able to do:
Compose followed by _ followed by A followed by E => ǣ

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Thank you; I followed the latter method. I'd've upvoted you had I been able to but you'll have to make do with the knowledge that you've helped someone to copy out some tables of Old English inflexion/pronunciation. – Anagram Ataf Jun 10 '20 at 20:28
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@AnagramAtaf: Good to hear that you made it work. – Gunnar Hjalmarsson Jun 10 '20 at 20:39
This is what I get by first typing an æ, then pressing control-alt-u, then typing 304, and then pressing space: ǣ. It looks better in some fonts than in others. It might be possible to get the compose key to work the way you suggest, but I haven't tried it. For that, I'd read the answers to this other question: How can I add a custom compose key sequence? I hope that's enough, otherwise I hope someone can read those answers and adapt them for this.
Edit: As Gunnar Hjalmarsson says, you could press control-shift U, type 1e3, then press space, and that would write ǣ without having to type the æ as a separate character.
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1Please note that ǣ exists as unicode U01E3. So
+ – Gunnar Hjalmarsson Jun 10 '20 at 18:51+U followed by 01e3 works.