gesteigert
increased
Present to a higher or intensified degree; intensified.
Seit dem Vorfall hat sie ein gesteigertes Bedürfnis nach Sicherheit.
Since the incident, she has had an increased need for security.

increased
Loading your saved state.
increased
Present to a higher or intensified degree; intensified.
Seit dem Vorfall hat sie ein gesteigertes Bedürfnis nach Sicherheit.
Since the incident, she has had an increased need for security.

'Gesteigert' (increased) is the past participle of the verb 'steigern' (to increase, intensify). When it is used as an adjective, it keeps this meaning of 'increased' or 'intensified'.
Die Mannschaft zeigte in der zweiten Halbzeit eine gesteigerte Leistung.
The team showed an improved performance in the second half.
In everyday language, 'gesteigert' almost always means 'intensified' or 'increased'. The grammatical meaning is used only in specialist discussions about language.
Er hat ein gesteigertes Interesse an moderner Kunst.
He has an increased interest in modern art.
'Gesteigert' (increased) is often combined with abstract nouns to express a higher intensity. Typical examples are 'gesteigertes Interesse' (increased interest), 'gesteigerte Nachfrage' (increased demand), or 'gesteigertes Selbstvertrauen' (increased self-confidence).
Nach der Werbekampagne gab es eine gesteigerte Nachfrage nach dem Produkt.
After the advertising campaign, there was increased demand for the product.
This meaning is a technical term from grammar (linguistics). Outside of language classes or linguistics, this meaning is not used.
Im Grammatikbuch wird die gesteigerte Form von Adjektiven erklärt.
The grammar book explains the comparative and superlative forms of adjectives.
increased / increasingly
'vermehrt' and 'gesteigert' can both express that something has become stronger or greater. 'vermehrt' is often used when something occurs more frequently or is present in greater numbers, for example 'vermehrte Anfragen' (increased inquiries). 'gesteigert' is more suitable when a measure, a force, or an intensity is higher, for example 'gesteigerte Aufmerksamkeit' (increased attention). Learners may confuse the words because both describe an increase. A practical tip: for frequency and number, 'vermehrt' often sounds more natural; for intensity or performance, 'gesteigert' often does.

Lukas zeigt seit dem Gespräch ein gesteigertes Interesse an der neuen Aufgabe.
Since the conversation, Lukas has shown an increased interest in the new task.
Zur Prüfungsvorbereitung nutzt der Kurs vermehrt kurze Übungen am Computer.
To prepare for the exam, the course is increasingly using short exercises on the computer.