geltend
valid / in force
Valid, in force, or effective. Used almost exclusively in reference to laws, rules, or regulations.
Nach geltendem Recht ist das Parken hier verboten.
Under current law, parking is prohibited here.

valid / asserted
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valid / in force
Valid, in force, or effective. Used almost exclusively in reference to laws, rules, or regulations.
Nach geltendem Recht ist das Parken hier verboten.
Under current law, parking is prohibited here.

'Geltend' is the present participle of the verb 'gelten' (to be valid, to apply). This origin explains the meaning 'being valid' or 'being in force'.
Diese Regel gilt für alle Mitarbeiter ohne Ausnahme.
This rule applies to all employees without exception.
In the meaning 'gültig' (valid), 'geltend' is used almost exclusively as an adjective before a noun (attributive use). Using it as a standalone predicate, e.g. 'Das Recht ist geltend.' (The law is valid/in force), is very unusual.
Bitte beachten Sie die geltenden Sicherheitsvorschriften.
Please observe the applicable safety regulations.
The word 'geltend' occurs very often in the fixed expression 'geltend machen' (to assert/claim). This means that someone formally demands a claim or right.
Der Anwalt riet ihm, Schadensersatzansprüche geltend zu machen.
The lawyer advised him to assert claims for damages.
What can you 'geltend machen' (assert/claim)? Typical objects are 'Ansprüche' (claims), 'Forderungen' (demands/claims), 'Kosten' (costs), 'Rechte' (rights), or more abstract things such as 'seinen Einfluss' (one's influence).
Viele Arbeitnehmer machen die Fahrtkosten zur Arbeit steuerlich geltend.
Many employees claim their commuting costs to work for tax purposes.
to demand / challenge
'fordern' and 'geltend machen' can both mean that someone demands something because they believe they have a right to it. 'fordern' is more direct and can fit many situations, for example with money, help, or better rules. 'geltend machen' is more formal and is used especially for rights, claims, or demands, often in contracts, with authorities, or in court. The words can be confused because both involve demanding something. However, 'geltend machen' does not sound like an ordinary wish, but like an official claim.

Julia macht nach dem Unfall ihren Anspruch auf Schadenersatz geltend.
After the accident, Julia asserts her claim for compensation.
Die Mieter fordern eine schnelle Reparatur der Heizung.
The tenants are demanding a quick repair of the heating.